IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1 Hybrid-hypergraph Regularized Multi-view Subspace Clustering for Hyperspectral Images Shaoguang Huang, Member, IEEE, Hongyan Zhang, Senior Member, IEEE, and Aleksandra Piˇ zurica, Senior Member, IEEE Abstract—Clustering algorithms play an essential and unique role in classification tasks, especially when annotated data are unavailable or very scarce. Current clustering approaches in remote sensing are mostly designed for a single data source, such as hyperspectral image (HSI), while nowadays multi-sensor data are being routinely acquired. In this paper, we propose a multi- view subspace clustering model, which exploits effectively the rich information from multiple features extracted either from a single data source (HSI) or from multiple sources, that we call generically multi-views of the same scene. An important novelty of our approach is that it integrates local and nonlocal spatial information from each view in a unified framework. Our model learns a common intrinsic cluster structure from view- specific subspace representations by a new decomposition-based scheme. In addition, we develop innovative manifold-based spatial regularization as a hybrid hypergraph, which merges local and non-local spatial context and improves thereby the learning of view-specific structures. We develop an efficient algorithm to solve the resulting optimization problem. Extensive experiments on real datasets demonstrate the superior clustering performance over the state-of-the-art. Index Terms—Hyperspectral images, remote sensing, subspace clustering, multi-view clustering. I. I NTRODUCTION H YPERSPECTRAL imaging systems measure the light reflected from objects in hundreds of spectral bands, covering the spectral range from visible to near-infrared. This wealth of spectral information enables far better discrimina- tion between diverse materials compared to traditional color and multispectral images. Consequently, hyperspectral images (HSIs) find numerous applications in remote sensing, in the domains such as precision agriculture [1, 2], defense and security [3], geology and mineralogy [4] and environmental monitoring [5, 6]. In all these applications, image classifica- tion, as a fundamental step in data preprocessing, provides a basis for the automatic HSI analysis and scene interpretation. Over the last two decades, a number of supervised classi- fication methods for HSIs have been proposed [7–9]. Some of the most prominent approaches are based on random This work was supported in part by the Flanders AI Research Programme under the grant 174B09119 and in part by the National Natural Science Foun- dation of China under the grants 61871298 and 42071322. (Corresponding author: Hongyan Zhang.) S. Huang and A. Piˇ zurica are with the Department of Telecom- munications and Information Processing, TELIN-GAIM, Ghent Univer- sity, 9000 Ghent, Belgium (e-mail: Shaoguang.Huang@ugent.be; Aleksan- dra.Pizurica@ugent.be). H. Zhang is with the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China (e-mail: zhanghongyan@whu.edu.cn). forests [10], support vector machine [11], sparse representation classification [12] and the recently arisen deep neural networks [13]. All these rely on labeled training samples to optimize the delicately designed classifiers. Since data labeling is typically labor intensive and time-consuming, labeled data required for training the classifiers are often scarce, posing serious limitations for the supervised classification methods [14]. In contrast, clustering, as an unsupervised approach, aims to discriminate data points belonging to different clusters without using any labeled data. Thus, clustering enables automatic data processing and interpretation in cases where supervised classification is infeasible. This is especially of interest in dynamic scenarios like monitoring forest fires and disaster damages where clustering plays a unique role [15]. Common clustering approaches include hierachical clus- tering [16, 17], centroid-based [18–22], density-based [23], biological clustering [24] and spectral-based methods [25– 29]. Spectral-based clustering methods, which are of special interest here, consist of two steps: construction of a similarity matrix and spectral clustering. A large body of the litera- ture has focused on building a desirable similarity matrix. Representative methods are low-rank representation (LRR) model [27] and sparse subspace clustering (SSC) model [28]. While these approaches achieved great success in computer vision, their direct appliction in HSI clustering often yields unsatisfactory results, due to various reasons, including noise, within-class spectral variability and complex data structure [30, 31]. Various extensions of subspace clustering have been de- veloped to alleviate these problems. Incorporating spatial information in the SSC model by using smoothing strategies in a local square window as proposed in [30] proved to be effective. Several follow-up works [32–35] exploit the spatial information using other types of spatial regularization, such as ℓ 2 norm-based smoothing term [32], joint representation [33] and total variation [34, 35]. An alternative to integrating spatial regularizations into the learning model is post-processing of the representation coefficients as in [36, 37]. Other repre- sentative approaches [38–40] build an anchor-based graph with a few initially selected samples with the aim to reduce the overall computational complexity of SSC. Generalizations to semi-supervised clustering models include [41, 42] and parameter-free multi-objective SSC was proposed in [43]. While achieving improved clustering performance, the above mentioned SSC-based clustering methods still face two crucial limitations. Firstly, they incorporate only local spatial content from windows of fixed size at a single particular scale.